After losing Rory McArdle to illness the morning of the game, City found themselves behind with less than ninety seconds on the clock when Shrewsbury striker Tom Bradshaw headed in from close range.
To make matters worse, City's efforts to get back in the match were hindered further when top scorer Nahki Wells was forced to limp off with an ankle injury midway through the first half.
Much to the delight of Parkinson, however, the Bantams refused to feel sorry for themselves as they forced Shrewsbury back time after time in the second period.
Kyel Reid netted City's equaliser on the hour mark before James Hanson swooped to seal a dramatic victory with the all-important winner in the fourth and final minute of injury time.
Parkinson said: "It is a great three points for us.
"Conceding the early goal, losing Rory the morning of the match, Nahki going off injured - it wasn't going our way.
"But we said to the lads at half time that we didn't want this to be a day where we were searching out for excuses as to why it didn't go for us.
"We didn't want to feel sorry for ourselves, we needed people to step up and be counted, and the lads certainly did that.
"To win like we did at the end there, it is a great reward for them.
"We pinned them in for the second half apart from a couple of isolated chances on the break, but you always run the risk of that happening against you when you throw men forward like we did.
"You could feel it in the stadium. The fans never stopped believing because they know we have the ability to produce something even right at the end. They know that we have a group of players here that will keep going.
"I felt after we conceded in the first half there was a bit of a period where we became a bit frantic, giving some fouls away. Not so much frantic in our play, but a bit frantic in our minds.
"We got everything calmed down at half time and told the lads that we still have forty-five minutes to win this. We said that if we kept playing with a calmness and kept getting the ball to our wide players and into Mark Yeates' feet, we'd have a real chance.
"It is too easy in football to have an excuse or an issue to fall back on - we certainly weren't going to let that happen.
"The lads in the dressing room certainly weren't going to accept that."
Reid and Hanson's second half strikes were the duo's second and fourth goals of the season respectively. Parkinson was particularly pleased to see the pair find the net after hard-working displays.
He added: "Reidy (Kyel Reid) will take his game up to another level by scoring goals like he did today (Saturday).
"He needs to get into the eighteen yard box when crosses are coming from the other side, and that's what he's done today.
"In the past, he has been guilty of standing outside the box in similar situations when goals are normally scored inside the area.
"So I was pleased to see Reidy get his goal today - it was a reward for a terrific all-round display from him.
"With James, he ran himself into the ground for the team in the second half.
"To get the goal at the end was great for him."